An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise to a probability distribution P(X)=|ψ(x)|^2 for the position of the particle X. For a specific harmonic oscillator potential, the wavefunction is given by: ψ(x)=(1/4*(2π)^1/4)e^(−x^2−4x+4/1024) By calculating |ψ(x)|^2 and rearranging
An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise to a probability distribution P(X)=|ψ(x)|^2 for the position of the particle X. For a specific harmonic oscillator potential, the wavefunction is given by: ψ(x)=(1/4*(2π)^1/4)e^(−x^2−4x+4/1024) By calculating |ψ(x)|^2 and rearranging
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise to a probability distribution P(X)=|ψ(x)|^2 for the position of the particle X. For a specific harmonic oscillator potential, the wavefunction is given by:
ψ(x)=(1/4*(2π)^1/4)e^(−x^2−4x+4/1024)
By calculating |ψ(x)|^2 and rearranging the exponent, convince yourself that P(X) can be written as a properly normalised Gaussian distribution.
(a) Find the mean μ of P(X)
(b) Find the standard deviation σ of P(X)
(c) Find the value of c such that P(X>c)=4P(X≤c)
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